How do I approach a Girl who travels on the mutual route and is in my batch?

When i started going to my newly joined coaching centre, i noticed a girl at the Metro Station (its like India's Subway), very cute though. And, coincidentally she was in my batch only (a batch of 400).

Day after day i realised that she boards at the same station that i board from and we arrive at the station at almost the same time. But she usually takes Coach 1 (reserved for Ladies) and i have to board the Coach 2. I respect that since she would want her safety first.

We do have eye contacts before the Metro Train arrives to which i respond by smiling. (Should i do that?)

Next thing is the most common thing in a story, she usually sits with a boy (school friends, i guess)

so i can't go and sit next to her and start a conversation.

And ofcourse, while returning home, we board the same train at the same station.